A fund manager has a well-diversified portfolio that has a beta of 1.5 (measured against the S&P/TSX 60 index) and is worth $500 million. The S&P/TSX 60 index is currently standing at 1,500. The manager would like to buy insurance against a reduction of more than 5% in the value of the portfolio (excluding dividends) over the next 3 months. The risk-free rate is 2% per annum. The dividend yield on the portfolio and the index is 3%. The volatility of the index is 30%. All rates are compounded continuously.

a) If the fund manager buys index put options (with European exercise style), how much would the insurance cost?

b) If the fund manager decides to provide insurance by keeping part of the portfolio in risk-free securities, what should the initial position be?

c) If the fund manager decides to provide insurance by using 6-month index futures, what should the initial position be?